Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows

Abstract

The main purpose of this paper is to describe a finite element formulation for solving the equations for $k$ and $\varepsilon$ of the classical $k-\varepsilon$ turbulence model, or any other two‐equation model. The finite element discretization is based on the SUPG method together with a discontinuity capturing technique to deal with sharp internal and boundary layers. The iterative strategy consists of several nested loops, the outermost being the linearization of the Navier–Stokes equations. The basic $k-\varepsilon$ model is used for the implementation of an algebraic stress model that is able to account for the effects of rotation. Some numerical examples are presented in order to show the performance of the proposed scheme for simulating directly steady flows, without the need of reaching the steady state through a transient evolution.